Abstract. The problem on radial oscillations of an elastic cylinder with inhomogeneous residual stress (RS) is considered. Two acoustic techniques of RS reconstructing are suggested. Within the framework of the first method, a set of radial displacement values is assumed to be known, while the frequency is fixed. Within the framework of the second method, the radial displacement value at the outer radius is assumed to be known for a set of frequencies. The examples of numerical identification experiments are presented.
Problem statementThe motion equations, constitutive relations, and mixed boundary conditions describing steadystate vibrations of isotropic body under residual stress state (RSS) have form [1,2]: e T e e T e e T T r r r r r r rre e e e e e e r r r r r r rr 0 0 0 0 01 1 . r r r r r r r u u u u u e e e e u e e u e e r r r rAs a particular practical example of the statement presented let us consider axisymmetric problem on steady-state vibration of a cylindrical region (inner radius 0 1 > r , outer radius
We propose a scheme of efficient solving an inverse coefficient problem on a reconstruction of unknown laws of variation of mechanical properties of inhomogeneous isotropic cylindrical region. The reconstruction is performed step‐by‐step by means of solving two problems on torsional and radial vibrations of the considered region that provides a formulation of two inverse problems on searching the unknown functions. We build iterative processes of solving the inverse problems stated; in frames of each process, we derive systems of the Fredholm integral equations of the 1st and the 2nd kind in order to find corrections to the unknown functions relative to the corresponding initial approximations. We conduct the computational experiments on a reconstruction of the unknown dimensionless functions.
In this study, modelling and identification of prestress state in functionally graded plate within the framework of the Timoshenko theory are discussed. With the help of variational principles, statements of boundary problems for stationary vibration of inhomogeneous prestressed plates have been derived taking into account various factors of prestress state. The comparative analysis of classical and nonclassical models has been conducted. The effect of the prestress state factors on the solution characteristics has been estimated. New approaches to solving the inverse problems on a reconstruction of inhomogeneous prestress functions in a functionally graded plate have been proposed on the basis of derivation of reciprocity relations and iterative regularization. The results of numerical reconstruction experiments are presented; practical recommendations on a selection of frequency range for the purpose of getting the highest reconstruction accuracy are given.
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